Academic literature on the topic 'Backward recurrence times'

Abstract It has been indicated in the literature to many factors that contribute to faults in rotor dynamical systems such as rubbing impact at stator-rotor contact. Accordingly, the appearance of rubbing impact is investigated here as one of the major factors that could excite the post-resonance backward whirl (Po-BW) phenomena in rotors. Therefore, the effect of rotor-stator rub impact on Po-BW excitation is numerically studied here with a Jeffcott rotor model. Accordingly, vertical and horizontal rotor configurations are considered here with rub-impact. The rubbing between the stator and the rotor is modeled by using both Heaviside function and the exact time calculation during the numerical simulation for comparison and to guarantee whirl results convergence. It is found that at a time step of order 10−6 in the numerical integration both Heaviside function and exact contact time calculations produce similar convergent results. In addition, the obtained numerical simulation results show that the stator-rotor rub-impact is found to excite the Po-BW and affects their recurrence and intensity. Accordingly, the current study provides a more insight to the impact of rotor-stator rubbing on Po-BW excitation. Therefore, the rotor-stator rub-impact is found to be one of the main factors that lead to excite the Po-BW during the rotor transient operation.

The Dirichlet Belief Network~(DirBN) has been recently proposed as a promising approach in learning interpretable deep latent representations for objects. In this work, we leverage its interpretable modelling architecture and propose a deep dynamic probabilistic framework -- the Recurrent Dirichlet Belief Network~(Recurrent-DBN) -- to study interpretable hidden structures from dynamic relational data. The proposed Recurrent-DBN has the following merits: (1) it infers interpretable and organised hierarchical latent structures for objects within and across time steps; (2) it enables recurrent long-term temporal dependence modelling, which outperforms the one-order Markov descriptions in most of the dynamic probabilistic frameworks; (3) the computational cost scales to the number of positive links only. In addition, we develop a new inference strategy, which first upward-and-backward propagates latent counts and then downward-and-forward samples variables, to enable efficient Gibbs sampling for the Recurrent-DBN. We apply the Recurrent-DBN to dynamic relational data problems. The extensive experiment results on real-world data validate the advantages of the Recurrent-DBN over the state-of-the-art models in interpretable latent structure discovery and improved link prediction performance.

The paper presents a gradient-based numerical algorithm for optimal control of nonlinear multivariable systems with control and state vectors constraints. The algorithm has a backward-in-time recurrent structure similar to the backpropagation-through-time (BPTT) algorithm, which is mostly used as a learning algorithm for dynamic neural networks. This paper presents an enhancement of the basic optimization algorithm. Our enhanced algorithm uses high-order Adams time-discretization schemes instead of the basic Euler discretization method, and a numerical calculation of Jacobians as an alternative to analytical Jacobians. Two examples are considered to illustrate the algorithm and its performance. The first example is that of a tubular reactor, for which an analytical solution is available, which can be readily used for validation of our approach. The second example is related to controlling vehicle dynamics based on a realistic high order model.